Hundreds have been reportedly killed on both sides as Afghan resistance forces hold out the Panjshir Valley against the Taliban.
The Taliban claim to have reclaimed a lot of territory and inflicted “heavy” losses on the National Resistance Front (NRF).
However, the NRF said it had control of all entrances to the valley, and the Taliban had lost hundreds of fighters.
Panjshir is the only province that has not fallen to the Islamist group and thousands of opposition fighters are believed to have massed there.
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The resistance – which includes former Vice-President Amrullah Saleh, former Afghan security force members and local militias – is led by local tribal leader Ahmad Massoud. Massoud’s father held off the Soviets in the 1980s and the Taliban in the 1990s.
Meanwhile US President Joe Biden visited troops who were injured in a devastating bomb attack at Kabul airport as they helped to evacuate Americans and Afghans from the country. Thirteen US soldiers were among some 170 people killed.
He made the visit four days after the last American soldiers left Afghanistan, where the Western-backed government had crumbled in the face of a Taliban offensive this summer.
Biden has been criticised for his decision to withdraw troops from Afghanistan and for the way that he has overseen the events of the past few weeks.
His visit to the hospital is a way for him to pay tribute to the sacrifices that people have made. It is also a reminder of the cost of war, and why he said the US should leave Afghanistan.
White House officials carried big bouquets of flowers inside the hospital, to help brighten the rooms of the injured men and women.
Taliban spokesman Zabihullah Mujahid said that fighters had moved into the Panjshir Valley after negotiations failed, Reuters news agency reports.
Talks failed because the two sides held very different positions, BBC Persian quoted NRF spokesman Fahim Dashti as saying.
He said they were fighting the Taliban on two fronts and that 350 Taliban fighters had been killed and a number captured.
Claims from either side are difficult to verify.
Reports of Taliban fighters searching for, and killing, people such as senior police officials and government officials contradict the more moderate image the group sought to portray when it took control of the country.
